One angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches. What is the area of the parallelogram? Express your answer in simplest radical form.
Explanation: [asy]
pair A,B,C,D,X;
A = (0,0);
B= (15,0);
D = rotate(60)*(8,0);
C = B+D;
X = (4,0);
draw(X--A--D--C--B--X--D);
label("$A$",A,SW);
label("$D$",D,NW);
label("$C$",C,NE);
label("$B$",B,SE);
label("$X$",X,S);
[/asy]

If one angle of the parallelogram is 120 degrees, then another angle between adjacent sides has measure $180^\circ - 120^\circ = 60^\circ$.  Shown in the diagram above, let the parallelogram be $ABCD$, with $\overline{AD}$ one of the short sides.  Drawing the altitude from $D$ to $\overline{AB}$ gives us 30-60-90 triangle $AXD$, from which we find $XD = (AD/2)\sqrt{3} = 4\sqrt{3}$, so the area of $ABCD$ is $(AB)(XD) = \boxed{60\sqrt{3}}$.